Waldyr Muniz Oliva, Brazilian mathematician (Santos, São Paulo State 16 June 1930 –

DEVELOPED CONCEPTS AND DEFINITIONS

Introduced Birkhoffian at finite or infinite dimensions

Introduced the concept of the attractor of a retarded functional differential equations

Proposed the specific notion of compact global attractor (1970s)

Une definition équivalente à l’involution de E. Cartan pour les systemes d’equations aux derivées partielles. Cahiers Topol. Geom. Diff. Categor. 11(2):201-5, 1969

CONTRIBUTIONS

Presented a characterization for the notions of regular and singular curves

With I. Kupka. The non-holonomic mechanisms. J. Diff. Equations 169(1):169-89, 2001

Presented a mathematical model for analyzing population dynamics involving human and mosquitoes

With E.M. Sallum. Periodic dynamic systems for infected hosts and mosquitoes. Rev. Saude Publica 30(3):218-23, 1996

Presented a new non-integrability approach

On the chaotic behavior and non-integrability of four vortices problem. Ann. Inst. Henri Poincaré 55:707-18, 1991

First to establish a sample path LDP for an SDDE with additive noise 

With R. Langevin & J.C.F. Oliveira. Retarded functional differential equations with white noise perturbations (1991)

Constructed a new class of Morse-Smale systems

With G. Fusco. Jacobi matrices and transversality. Proceed. Royal Soc. Edinburgh Sec. A. Math (1988)

DEVELOPED THEOREMS

With P. Duarte & R.L. Fernandes. Dynamics of the attractor in the Lotka-Volterra equations. J. Diff. Equations 149(1):143-89, 1998

With N.M. Kuhl & L.T. Magalhães. Diffeomorphisms of Rⁿ with oscillatory jacobians. Publ. Matem. 437:255-69, 1993

With G. Fusco. A Perron theorem for the existence of invariant subspaces. Ann. Math. Pura Appl. (1991)

Functional differential equations on compact manifolds and an approximation theorem. J. Diff. Equations 5:483-96, 1969